I came across a listing for Robert Pattinson “The Childhood of a Leader” at Art House – Crouch End Cinema, London from 22 July 2016.  I contacted them and they have confirmed to RPAU that the film will indeed screen from Friday 22 July 2016 and that tickets will go on sale 18 July 2016. Keep a watch out for them here.
UPDATED: 20 JULY 2016
Looks like Art House has pushed back their release by one week.  The Childhood of a Leader is now showing from 29 July 2016
UPDATED: 26 July 2016
Art House is now showing the release date as per the UK date of 19 August 2016